A cannon ball is fired so that it hits the wall at the top of a 10m tower.If the energy needed to destroy the wall is 49000 F and the mass of the cannon ball is 10 k, the minimum initial velocity of the cannon ball required to break the tower wall is
A 100 m/s
b 200 m/s
c 300 m/s
d 400 m/s
my way:
WD against friction + PEgain =KEloss
49000 + 10*10*10=1/2*(10)(u)^2 - 0
but is that way right?
who can told me the right one?
and if mine is correct,what is the principle behind?
why energy needed is equal to wd against friction?
You have done it well, the principle is conservation of energy: the energy at the top of the wall (PE+KE) is equal the the original energy.
but if i do that,then does it mean that i only supply 49000J to only overcome the work done agaist friction?
the initial KE goes into raising the cannonon ball to the height of 10 m, and then giving it energy to break the wall. Yes, at the top it has KE to break the wall of 49000J.
Your approach is partially correct, but let's go through the calculations step by step to find the minimum initial velocity of the cannonball required to break the tower wall.
First, let's consider the energy conservation principle. The energy needed to destroy the wall is equal to the work done against friction plus the potential energy gained by the cannonball:
Energy needed = Work against friction + Potential energy gained
In this case, the work done against friction can be neglected because it is not given in the problem statement. So, we have:
Energy needed = Potential energy gained
The potential energy gained by the cannonball is equal to the change in potential energy as it rises up to hit the wall:
Potential energy gained = mgh
where m is the mass of the cannonball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the tower (10 m in this case). Substituting the given values:
Potential energy gained = (10 kg)(9.8 m/s^2)(10 m) = 980 J
Now, let's equate the energy needed to the potential energy gained:
49000 J = 980 J
The left-hand side represents the energy needed to destroy the wall, which is given as 49000 J. However, you made a mistake in calculating the right-hand side.
Since the energy needed and the potential energy gained should be equal, the minimum initial velocity of the cannonball required to break the tower wall can be found using the principle of conservation of energy. Based on the calculation above, the correct answer is:
Minimum initial velocity = sqrt(2gh) = sqrt(2*9.8*10) ≈ 14 m/s
Therefore, none of the options A, B, C, or D match the correct answer.
To summarize:
- Your approach was correct in considering the conservation of energy.
- The principle behind equating the energy needed to work done against friction is that any energy lost due to friction would be converted into work and must be accounted for in the calculation.
- However, in this problem, the work done against friction is not given, so we can neglect it.
- The minimum initial velocity can be calculated by equating the energy needed to the potential energy gained by the cannonball.
- The correct minimum initial velocity to break the tower wall is approximately 14 m/s.